Though not as widely known as the classical EPI of Shannon and Stam, Costa's
EPI has found useful applications in deriving capacity bounds for the Gaussian
interference channel [1]} and the multiantenna flat-fading
channel [2]}. The original proof of Costa's EPI provided in
[3]} was based on rather detailed calculations. Simplified proofs
based on a Fisher information inequality [4]} and a fundamental
relationship between the derivative of mutual information and minimum
mean-square error (MMSE) in linear Gaussian channels [5]} can be
found in [6]} and [7]}, respectively.
